I personally don't think it's an intrinsic property of all matter, but an emergent one with interaction specifically. Systems have intelligence, not particles, and to be a system, you must have constituent parts (which may not be intelligent themselves). That's why they say it 'emerges'.

A cell is a system, as is a virus, a tucan, a human and an LLM. They exhibit different levels and brands of intelligence, hence continuum.

That's the popular view among scientists/philosophers/my podcasters, at least, and it makes sense to me!

No, intelligence is a description of behavior, not stuff.

As a crisp example: a newly dead person is almost exactly the same stuff as an alive person, but has no intelligence at all. Not a little less, as the difference in stuff would suggest.